arXiv subjects

Manuel Weiß

Publications and source records attributed to Manuel Weiß.

5 recordsLinked to original sources

arXiv2026

Geometry Denoising with Preferred Normal Vectors

We introduce a new paradigm for geometry denoising using prior knowledge about the surface normal vector. This prior knowledge comes in the form of a set of preferred normal vectors, which we refer to as label vectors. A segmentation problem is naturally embedded in the denoising process. The segmentation is based on the similarity of the normal vector to the elements of the set of label vectors. Regularization is achieved by a total variation term. We formulate a split Bregman (ADMM) approach to solve the resulting optimization problem. The vertex update step is based on second-order shape calculus. We present various examples including the denoising of an eroded medieval gravestone inscription.

cs.CV↗

arXiv2026

Two Models for Surface Segmentation using the Total Variation of the Normal Vector

We consider the problem of surface segmentation, where the goal is to partition a surface represented by a triangular mesh. The segmentation is based on the similarity of the normal vector field to a given set of label vectors. We propose a variational approach and compare two different regularizers, both based on a total variation measure. The first regularizer penalizes the total variation of the assignment function directly, while the second regularizer penalizes the total variation in the label space. In order to solve the resulting optimization problems, we use variations of the split Bregman (ADMM) iteration adapted to the problem at hand. While computationally more expensive, the second regularizer yields better results in our experiments. In particular it removes noise more reliably in regions of constant curvature. In order to mitigate the computational cost, we present a manifold Newton scheme for the most expensive subproblem, which is related to the Riemannian center of mass on a sphere. This significantly improves the computational cost.

cs.CV↗

arXiv2025

Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising

We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV models for piecewise constant scalar data that utilize a Raviart-Thomas function space. To extend this formulation to the manifold setting, a tailor-made tangential Raviart-Thomas type finite element space is constructed in this work. The new regularizer is compared to existing methods in mesh denoising experiments.

cs.CV↗

arXiv2024

Mesh Denoising and Inpainting using the Total Variation of the Normal and a Shape Newton Approach

We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total variation of the unit normal vector field serves as a regularizing functional to achieve these goals. In order to solve the resulting problem, we use a version of the split Bregman (ADMM) iteration adapted to the problem. A new formulation of the total variation regularizer, as well as the use of an inexact Newton method for the shape optimization step, bring significant speed-up compared to earlier methods. Numerical examples are included, demonstrating the performance of our algorithm with some complex 3D geometries.

math.NA↗

arXiv2023

The Proximal Map of the Weighted Mean Absolute Error

We investigate the proximal map for the weighted mean absolute error function. An algorithm for its efficient and vectorized evaluation is presented. As a demonstration, this algorithm is applied as part of a checkerboard algorithm to solve a total-variation image denoising (ROF) problem as well as a non-smooth energy minimization problem.

math.OC↗